The theory of quantum error correction (QEC) [1]} lays down the basic framework for dealing with noise affecting the quantum states of interest. The early works of Shor [2]}, [3]} and Steane [4]} demonstrated how quantum error correcting codes can be constructed for bit-flip and phase-flip noise, by making use of entanglement to circumvent the challenge posed by no-cloning theorem [5]}. Subsequently, a general theory of QEC was developed for arbitrary errors, in terms of algebraic [6]} and information-theoretic conditions [7]}. Today, the standard approach to quantum error correction works by discretizing the errors affecting the quantum state in terms of the Pauli basis [8]}, with the group structure of the Pauli operators naturally leading to the rich mathematical framework of quantum stabilizer codes [9]}. We refer to a recent review [10]} that surveys the major developments in QEC, from the stabilizer codes and CSS codes to the more recently proposed classes of topological codes [11]} and surface codes [12]}.
